Computerized models of the left ventricle are being developed for the purpose of evaluating myocardial function. These models are based on a rigorous treatment of nonlinear elasticity theory. To date, most of the effort has been devoted to an analysis of diastolic stiffness and fiber elongation. However, the systolic portion of the cardiac cycle will be emphasized in future studies. A constitutive relation has been developed for uniaxial, afterloaded-isotonic contractions of cardiac muscle. Multiple-dimension generalizations of this relation will be incorporated into the passive constitutive relations for the myocardium, and time-dependent values of transmural pressure and cavity volume will be related to myocardial stress and deformation via the equilibrium equations for an elastic solid of revolution. The resulting dynamic models will be used to evaluate certain parameters in the constitutive relations which have been identified as indices of myocardial function.